MLRATE

set.seed(1)

require(plotly)

Loading required package: plotly
Loading required package: ggplot2

Attaching package: ‘plotly’

The following object is masked from ‘package:ggplot2’:

    last_plot

The following object is masked from ‘package:stats’:

    filter

The following object is masked from ‘package:graphics’:

    layout

n = 21
x = rnorm(n,0,3)
v = round(runif(n))
y = 1*v + 1*x + rnorm(n,0,1)

variant <- (y-predict(lm(y~v),newdata=data.frame(v=0)))[v == 1]
control <- (y-predict(lm(y~v),newdata=data.frame(v=0)))[v == 0]
variant_d <- density(variant)
control_d <- density(control)

variant2 <- (y-predict(lm(y~v+x),newdata=data.frame(x=x,v=0)))[v == 1]
control2 <- (y-predict(lm(y~v+x),newdata=data.frame(x=x,v=0)))[v == 0]
variant2_d <- density(variant2)
# variant2_d$y <- variant2_d$y/sum(variant2_d$y)
control2_d <- density(control2)
# control2_d$y <- control2_d$y/sum(control2_d$y)

p1 <- plotly::plot_ly(type = 'scatter', mode= 'markers') %>%
  add_trace(y = x[v==0],x=y[v==0],color='#00263D',showlegend = F) %>%
  add_trace(y = x[v==0],x = predict(lm(y~v),newdata=data.frame(v=rep(0,length(x[v==0])))),
            name='Control',color='#00263D',mode='line',
            error_x = list(
              type='data',symmetric=FALSE,thickness=0.7,
              array=y[v==0]-predict(lm(y~v),newdata=data.frame(v=0))
              )
            ) %>%
  add_trace(y = x[v==1],x=y[v==1],color='#00253C',showlegend = F) %>%
  add_trace(y = x[v==1], x = predict(lm(y~v),newdata=data.frame(v=rep(1,length(x[v==1])))),
            name='Variant',color='#00253C',mode='line',
            error_x = list(
              type='data',symmetric=FALSE,thickness=0.7,
              array=y[v==1]-predict(lm(y~v),newdata=data.frame(v=1))
            )
  ) %>% layout(yaxis= list(title='Relevant covariate',showticklabels = FALSE))

p2 <- plotly::plot_ly(type = 'scatter', mode= 'markers') %>%
  add_trace(y = x[v==0],x=y[v==0],color='#00263D',showlegend = F) %>%
  add_trace(y = x[v==0],x = predict(lm(y~v+x),newdata=data.frame(v=0,x=x[v==0])),
            name='Control',color='#00263D',mode='line',showlegend = F,
            error_x = list(
              type='data',symmetric=FALSE,thickness=0.7,
              array=y[v==0]-predict(lm(y~v+x),newdata=data.frame(v=0,x=x[v==0]))
            )
  ) %>%
  add_trace(y = x[v==1],x=y[v==1],color='#00253C',showlegend = F) %>%
  add_trace(y = x[v==1], x = predict(lm(y~v+x),newdata=data.frame(v=1,x=x[v==1])),
            name='Variant',color='#00253C',mode='line',showlegend = F,
            error_x = list(
              type='data',symmetric=FALSE,thickness=0.7,
              array=y[v==1]-predict(lm(y~v+x),newdata=data.frame(v=1,x=x[v==1]))
              )
  ) %>%
  layout(yaxis = list(showticklabels = FALSE))
  
p3 <- plotly::plot_ly(type = 'scatter', mode= 'lines') %>%
  add_trace(x = y[v==0],type='histogram',histnorm = "probability",color='#00263D',showlegend = F) %>%
  add_trace(x = y[v==1],type='histogram',histnorm = "probability",color='#00253C',showlegend = F) %>%
  add_trace(x = control_d$x, y=control_d$y, fill = 'tozeroy',name='Control',color='#00263D',showlegend = F, yaxis = "y2") %>%
  add_trace(x = variant_d$x, y=variant_d$y, fill = 'tozeroy',name='Variant',color='#00253C',showlegend = F, yaxis = "y2") %>%
  layout(yaxis=list(title='Histogram <br> of samples',showticklabels = FALSE), yaxis2 = list(overlaying = "y3",
  side = "right",showticklabels=FALSE))
  
p4 <- plotly::plot_ly(type = 'scatter', mode= 'lines') %>%
  add_trace(x = control2,type='histogram',histnorm = "probability",color='#00263D',showlegend = F) %>%
  add_trace(x = variant2,type='histogram',histnorm = "probability",color='#00253C',showlegend = F) %>%
  add_trace(x = control2_d$x, y=control2_d$y,fill = 'tozeroy',name='Control',color='#00263D',showlegend = F, yaxis = "y2") %>%
  add_trace(x = variant2_d$x, y=variant2_d$y,fill = 'tozeroy',name='Variant',color='#00253C',showlegend = F, yaxis = "y2") %>%
  layout(yaxis = list(showticklabels = FALSE), yaxis2 = list(overlaying = "y5",side = "right",showticklabels=FALSE))


p5 <-  plotly::plot_ly(type = 'scatter', mode= 'lines') %>%
  add_trace(x = seq(min(y[v==0]),max(y[v==0]),0.01), y = dnorm(x = seq(min(y[v==0]),max(y[v==0]),0.01), mean = mean(y[v==0]), sd = sd(control)/sqrt(sum(v==0))), fill = 'tozeroy',name='Control',color='#00263D',showlegend = F) %>%
  add_trace(x = seq(min(y[v==0]),max(y[v==0]),0.01), y = dnorm(x = seq(min(y[v==0]),max(y[v==0]),0.01), mean = mean(y[v==1]), sd = sd(variant)/sqrt(sum(v==1))), fill = 'tozeroy',name='Control',color='#00253C',showlegend = F) %>%
  layout(xaxis = list(title = 'Typical A/B test: no variance reduction'), yaxis = list(title = 'Est. sampling <br> dist. of means',showtickLabels=FALSE))

p6 <-  plotly::plot_ly(type = 'scatter', mode= 'lines') %>%
  add_trace(x = seq(min(y[v==0]),max(y[v==0]),0.01), y = dnorm(x = seq(min(y[v==0]),max(y[v==0]),0.01), mean = mean(y[v==0]), sd = sd(control2)/sqrt(sum(v==0))), fill = 'tozeroy',name='Control',color='#00263D',showlegend = F) %>%
  add_trace(x = seq(min(y[v==0]),max(y[v==0]),0.01), y = dnorm(x = seq(min(y[v==0]),max(y[v==0]),0.01), mean = mean(y[v==1]), sd = sd(variant2)/sqrt(sum(v==1))), fill = 'tozeroy',name='Control',color='#00253C',showlegend = F) %>%
  layout(xaxis = list(title = 'Linear Variance reduction'), yaxis = list(showticklabels = FALSE))

subplot(p1,p2,p3,p4,p5,p6,nrows=3, shareY = F,shareX = T, titleX = T, titleY = T, margin = c(0.1,0,0.05,0))

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